Yes, you can store the Octave setting in OTS, but it is not done by simply switching the Octave setting on the keyboard. Here's a simple example that will show how it is done.
1. Copy the GrandPiano (I'll use this as an example voice), from the PRESET area to the USER area.
2. Use the Sound Creator to edit that GrandPiano voice. You'll see that the octave setting for the Main/Layer voice is one of the parameters. Change that to be -2 to move it down to octaves. Save this "modified" GrandPiano to the User area and give it a new name: GrandPiano-2 will do.
3. Edit the octave setting again and make it -1; save that voice to user memory as GrandPiano-1.
4. Try one more edit and set the octave to +1 and save that voice as GrandPiano1. You should now have 4 GrandPiano voices in your USER memory.
5. Now, as an example, store each of those GrandPiano voices into the 4 OTS settings. Select GrandPiano-2 as the MAIN voice; memorize that to OTS1. Select GrandPiano-1 as the MAIN voice; memorize that to OTS2. Put the normal GrandPiano in OTS3, and put GrandPiano1 in OTS4.
6. If you test out these settings, you will see that the GrandPiano voice shifts octaves as you go from OTS1 to OTS4.
7. SAVE the style you are using to floppy.
8. Switch to any other preset style to be sure you have your modified style out of memory. Now load the modified style back in from floppy.
9. If you check the OTS, they will all display as GrandPiano. But when you play them, each will be playinig at the octave you set them at. You do not need to have any of those modified voices saved in USER memory. You can delete all of them; the modified voice has been saved in the style.

Note: simply saving the style will save the OTS with the style. It is only if you Edit the style, that is change volume settings or put new instruments in the accompaniment, that you would have to use the Style Creator to SAVE the new style. If you are only modifying the OTS, you can just save the new style and the modified OTS is saved with it.

This works because Yamaha only saves the changes to the parameters you made in the Sound Creator. When you press that modified OTS, it first loads the preset GrandPiano, with all of its standard parameter settings, then it applies whatever changes to those parameters you made -- in this example, we changed the octave setting. The voice shows up on the screen as the preset voice "GrandPiano" but it plays as your modified voice.

Implications: If you modify a voice to suit your tastes, you do not have to keep it forever in the USER memory area; you can simply save it in the style.

If you do modify a voice and put it in the USER area, you can use it from there to put it in the OTS for a lot of styles. Your new voice is then available in all those styles.

Note: I would expect that this "technique" applies equally well to the CVP20x series and to the TYROS.